The Protection And Optimal Harvesting Problems For Biological Resource In Random Environment

Utilization of renewable biological resources has received great attention from theentire world since twentieth century. Based on mathematical models, this paper studiesthe protection and the optimal harvesting problems of biological resources theoretical-ly. Considering diferent types of environmental noise, this paper builds three stochasticmodels with protection zone, and studies the corresponding asymptotic properties. Thispaper also studies the optimal harvesting problems for two types of models with severalkinds of noise. The content of this paper includes the following several aspects:(1) The dynamical properties for a stochastic protection zone model with interfer-ence on single parameter which driven by both white noise and color noise. Using s-tochastic analysis techniques, some asymptotic properties are studied, such as persistenceand extinction. We analyze the positive efects of protection zone, give several measuresto improve the efects and get a method of dividing protection zone.(2) The dynamical properties for a stochastic protection zone model with interfer-ence on two parameters which driven by white noise. This model considers that twoparameters in the population growth model are disturbed by white noise. Through theresearch of a series of asymptotic properties for this model, we illustrate that the intrinsicgrowth rate of biological population is the most sensitive coefcient under environmentaldisturbance.(3) The dynamical properties for a stochastic protection zone model with interfer-ence on two parameters which driven by both white noise and color noise. We give anoverall analysis by synthesizing both (1) and (2). Results say establishing protection zonecan protect the biological population nicely under the random environment, and it alsocan slow down the speed of extinction under terrible circumstance.(4) Optimal harvesting problem for Gompertz models in random environment. Westudy the optimal harvesting problems for stochastic Gompertz models driven by Brownmotion and Le′vy process respectively. The equivalency of optimal harvesting problem-s under expectation and stationary probability density meanings is obtained by ergodicmethod. This paper applies ergodic method on the optimal harvesting problem.(5) Optimal harvesting problem for stochastic Logistic models. The optimal harvest-ing problems for stochastic Logistic models driven by Le′vy process and driven by both Le′vy process and Markov process are studied respectively. We show the equivalency ofobjective function on optimal harvesting problem between time average and stationaryprobability density meanings by ergodic method. This provide us a new idea for stochas-tic harvesting problem which can avoid the puzzle of solving Fokker-Planck equation.